Conditionally specified distributions: an introduction

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Modeling Discrete Interventional Data using Directed Cyclic Graphical Models (2009, unknown): “Closely related to dependency networks is the work of Hofmann and Tresp (1997), as well as work on conditionally specified distributions (Arnold et al., 2001; Heckerman et al., 2004) (and the references contained in these works).”
Maximum likelihood estimation using composite likelihoods for closed exponential families (2009, background): “Arnold & Strauss (1991b) and Arnold et al. (2001) investigated the construction of joint distributions given the conditionals and discussed various properties of such distributions.”
Efficient recursions for general factorisable models (2004, methodology): “For conditionals that are not derived from a known, though possibly unnormalised, joint distribution, compatibility must be checked; see for example Casella (1996) and Arnold et al. (2001).”
Efficient Thompson Sampling for Online Matrix-Factorization Recommendation (2015, unknown): “, [10, 11, 12] for more details).”
AN OVERVIEW OF COMPOSITE LIKELIHOOD METHODS (2011, background): “This issue is pursued in Wang and Ip (2008), where the key notion of interactions is defined, and their role in ensuring the compatibility of conditional and joint distributions is emphasized; see also Arnold et al. (2001). There is not an analogous result for composite marginal likelihood, although”